System bandwidth and the existence of generalized shift-invariant frames

We consider the question whether, given a countable family of lattices ${({\mathrm{\Gamma }}_j)}_{j\in J}$ in a locally compact abelian group G, there exist functions ${(g_j)}_{j\in J}$ such that the resulting generalized shift-invariant system ${(g_j(??\gamma ))}_{j\in J,\gamma \in {\mathrm{\Gamma }}_j}$ is a tight frame of $L^2(G)$. This paper develops a new approach to the study of generalized shift-invariant system via almost periodic functions, based on a novel unconditional convergence property. From this theory, we derive characterizing relations for tight and dual frame generators, we introduce the system bandwidth as a measure of the total bandwidth a generalized shift-invariant system can carry, and we show that the so-called Calder43;n sum is uniformly bounded from below for generalized shift-invariant frames. Without the unconditional convergence property, we show, counter intuitively, that even orthonormal bases can have arbitrary small system bandwidth. Our results show that the question of existence of frame generators for a general lattice system is rather subtle and depends on analytical and algebraic properties of the lattice system.     

Well‐posedness of fractional integro‐differential equations in vector‐valued functional spaces

We study the well‐posedness of the fractional differential equations with infinite delay on Lebesgue–Bochner spaces and Besov spaces , where A and B are closed linear operators on a Banach space X satisfying ,  and . Under suitable assumptions on the kernels a and b, we completely characterize the well‐posedness of 43383a-b926-4a5f-96b8-0077569008f9/mana201800104-math-0007.png"> in the above vector‐valued function spaces on by using known operator‐valued Fourier multiplier theorems. We also give concrete examples where our abstract results may be applied.     

发光颜色可调的白磷钙矿结构Ca8MgBi(PO4)7∶Ce3+，Tb3+荧光粉的制备、发光性能及能量传递

采用具有白磷钙矿结构的磷酸盐作为目标产物,通过高温固相法制备了发光颜色可调的Ca₈MgBi(PO₄)₇∶Ce³⁺,Tb³⁺荧光粉。利用X射线粉末衍射(XRD)、扫描电子显微镜(SEM)和荧光光谱等表征手段对其物相组成、微观形貌及发光性能进行了详细研究。结果表明：掺杂少量的Ce³⁺、Tb³⁺并没有改变Ca₈MgBi(PO₄)₇基质的晶体结构。荧光光谱和荧光寿命曲线确定了Ce³⁺-Tb³⁺之间存在能量传递,其能量传递机制为四极-四极相互作用,能量传递效率可达81%。固定Ce³⁺浓度而逐渐增加Tb³⁺的掺杂量时,系列Ca₈MgBi(PO₄)₇∶0.08Ce³⁺,yTb³⁺荧光粉的发...     

橙红色荧光粉Ca_(1-x-y)Sm_xBi_ySiO_3的制备及其发光性能

以Sm3+作为激活剂,Bi3+作为辅助激活剂,采用水热法合成Ca1-x-ySmxBiySi O3前驱体,然后在1 100℃焙烧得到系列橙红色荧光粉。用X-射线衍射仪、扫描电镜和荧光分光光度计和傅里叶变换红外光谱等手段对样品的组成、结构和形貌及其发光性质进行分析和表征。分析结果表明:产物都为三斜晶系结构的Ca1-x-ySmxBiySi O3和四方结构的方石英Si O2共熔体。在405 nm近紫外光激发下,产物的发射光谱由3个峰组成,发射峰值位于566、606和650 nm处,分别归属于Sm3+的4G5/2→6HJ/2(J=5,7,9)跃迁。产物的激发光谱在405 nm有很强的发射带,与近紫外LED芯片匹配。随着Sm3+掺量的增加,样品发光强度先增强后减弱,当Sm3+的物质的量分数为3%时发光强度达到最大,浓度猝灭机理为电偶极-电偶极相互作用。当Bi3+的物质的量分数在0.3%~1.5%时,对产物Ca0.97Sm0.03Si O3的荧光强度起敏化作用。Sm3+和Bi3+的最佳物质的量分数分别为3%和0.5%。     

TODGA/[C_2mim][NTf_2]萃取Th~(4+)

研究了N,N,N′,N′-四辛基-3-氧戊二酰胺(TODGA)溶于疏水性离子液体咪唑类离子液体1-乙基-3-甲基咪唑双三氟甲磺酰亚胺盐([C2mim][NTf2])中对硝酸水溶液体系中四价钍离子(Th4+)的萃取行为。详细考察了接触时间、酸度、Th4+浓度、TODGA浓度、温度对TODGA/[C2mim][NTf2]体系萃取性能的影响。作为对比,我们还考察了TODGA在传统有机溶剂异辛烷中对Th4+的萃取。结果表明:TODGA/[C2mim][NTf2]体系对Th4+的萃取是吸热反应,且在50℃下,能在5 min内达到平衡。萃取体系随着酸度对Th4+的萃取性能先降后增大;Th4+浓度的增大,TODGA浓度的降低,对Th4+的萃取性能下降。TODGA在离子液体萃取体系中比在有机体系中有更好的Th4+萃取效果,特别是在低酸条件下。通过萃取机理研究,推测出在低酸下萃取反应是离子交换且TODGA与Th4+配比为2∶1,在高酸下萃取是中性配位。     

一种应用于活细胞中检测Hg(Ⅱ)的苯并噻唑类荧光探针

合成和表征了一种苯并噻唑类的荧光探针(YH1),并用光谱法研究了它对不同金属离子的响应。结果表明:YH1对Hg2+显示出好的选择性和灵敏度,与Hg2+作用后,在紫外光的激发下它的溶液颜色由蓝色变为无色。在1.4~8.8μmol·L-1浓度的范围内,YH1的荧光强度与Hg2+浓度有线性关系,其对Hg2+的检出限为0.56μmol·L-1。此外,YH1可跨过细胞膜,细胞毒性低,还可应用于He La活细胞中对Hg2+进行荧光成像。     

A strict topology on Orlicz spaces

Let φ be a Young function, Ω be a locally compact space, and μ be a positive Radon measure on Ω. We consider a strict topology (in the sense of Sentilles‐Taylor) on the Orlicz function space and investigate various properties of this locally convex topology. We also study the Orlicz space of a locally compact group G with a left Haar measure under the strict topology and certain other natural locally convex topologies. Finally we present some results on various continuity properties of convolution operators on 435a-be17-e4b939522a04/mana201400100-math-0005.png"> under the topology and other natural ones.     

高色纯度高热稳定性红色荧光粉Sr3La2Ge3O12:Sm^3+的合成及其性能

通过高温固相法合成了一系列Sr3La2-xGe3O12:xSm^3+(0≤x≤0.04)红色荧光粉,并对样品的形貌、元素组成、晶体结构、发光性能及热稳定性进行了探究。结果表明:样品Sr3La2Ge3O12:xSm^3+为较宽尺寸分布的颗粒,且结构中仅含有Sr、La、Ge、O、Sm等元素。样品Sr3La1.97Ge3O12:0.03Sm^3+的Rietveld结构精修图与实测XRD图完全吻合,具有六方晶系结构。漫反射测试结果显示基质Sr3La2Ge3O12的带宽为5.54 eV,属于宽带隙材料。在404 nm激发下,样品Sr3La2-xGe3O12:xSm^3+(0≤x≤0.04)的最大发射峰位于601nm处,属于Sm^3+的6H5/2→4L13/2能级跃迁。此外,样品Sr3La1.97Ge3O12:0.03Sm^3+的发光性能最佳,其CIE色坐标为(0.5321,0.4601),色纯度高达94.2%,在298-473 K范围内具有较好的热稳定性,测试温度达到423 K时发射强度仍为室温时的81.6%。     

高光效高热稳定性蓝色荧光粉Ca2-ySrySiO4:Ce3+,Li+的组成筛选和发光机理

采用高温固相法合成了一系列Ca_(2-x-y)Sr_(y-x)SiO_4∶x Ce~(3+),x Li~+蓝色固溶体荧光粉。XRD结果表明,所合成的固溶体荧光粉均为单一物相。随着Sr~(2+)成分的增加,Ca_(2-y)Sr_y SiO_4物相从单斜晶系β-Ca_2SiO_4向正交晶系α′-Ca_2SiO_4转变,发射光谱逐渐红移。组成为Ca_(1.75)Sr_(0.25)SiO_4时,荧光粉的发射波长最长(454 nm),Stokes位移最大。基质为Ca_(1.1)Sr_(0.9)SiO_4的晶体结构可诱导掺杂离子Ce~(3+)取代SrO_(10)格位、Li~+取代CaO8格位。优化的荧光粉Ca_(1.05)Sr_(0.85)SiO_4∶0.05Ce~(3+),0.05Li~+(CS_(0.85)SO∶CeLi)在375 nm紫外光激发下,发射445 nm的蓝光,内量子效率(IQE)达到91.18%,200℃时发射强度保持室温发光强度的98.70%。根据晶体结构、晶体场分裂和掺杂离子质心位移等理论,讨论了CS_(0.85)SO∶CeLi综合发光效应最佳的内在原因。     

退火处理Fe43Co43Hf7B6Cu1非晶合金的正电子湮没研究

对熔体急冷法制备的Fe₄₃Co₄₃Hf₇B₆Cu₁非晶合金进行了200,300,400和500 ℃保温30 min的退火处理,用正电子湮没寿命谱、X射线衍射、穆斯堡尔谱等方法研究了退火后试样的结构及结构缺陷变化.结果表明,在非晶合金的制备态,正电子主要在非晶基体相空位尺寸的自由体积中湮没,湮没寿命τ₁为158.4 ps,强度I₁关键词： 43Co₄₃Hf₇B₆Cu₁非晶')" href="#">Fe₄₃Co₄₃Hf₇B₆Cu₁非晶 退火处理 正电子湮没寿命 结构与结构缺陷